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lfunc_lfunctions • Show schema
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{'Lhash': '3698421438915042087035060005527', 'a10': [-3.0, 3.111507638930571e-61], 'a2': [0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.5, -2.598076211353316], 'a6': [0.0, 0.0], 'a7': [0.5, -0.8660254037844386], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.55', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1580860621925003545434253845849', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.5, 0.8660254037844386], [-3.5, -6.06217782649107]], [[1.0, 0], [-1.5, 2.598076211353316], [-5.5, -9.526279441628825]], 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3.4460286591090075, 3.8711243865190634, 3.792109899332711, 3.212185877033927], 'positive_zeros': ['2.91754008419131711827962264885151', '4.20445647602309845509273962127230', '5.71641139191517235358585726381165', '6.90330704735414953485190453403468', '7.66905073689947661154738095313400', '8.834936174781593452814909941402732', '10.25053277570361930924207602017300', '11.23613223905438751972022657379443', '12.19283051970361002428092658245471', '13.20502644880271505762667057527525'], 'prelabel': '2-162-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.5555555555555556, 'root_number': '-0.1736481776669303 + 0.984807753012208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.277777777778', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.91754008419131711827962264885', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20445647602309845509273962127', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.71641139191517235358585726381', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/c/c/55/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-162-9.7-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-162-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.2777777777777778, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.91754008419131711827962264885', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3698421438915042087035060005527', 'Lhash_array': ['3698421438915042087035060005527'], 'label': '2-162-9.7-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/c/c/55/1'}